Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aji2)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.aji2.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(7/2), 11/2}, z] == (1/(32 z^4)) (-2116800 + 781200 z - 240120 z^2 + 59040 z^3 - 11892 z^4 + 2010 z^5 - 285 z^6 + 26 z^7 + 28 z^8 + 8 z^9) + (1/(64 z^(9/2))) (E^z Sqrt[Pi] (2116800 - 2192400 z + 1137240 z^2 - 393840 z^3 + 102420 z^4 - 21330 z^5 + 3705 z^6 - 552 z^7 + 72 z^8 + 64 z^9 + 16 z^10) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]